pGQL: A probabilistic graphical query language for gene expression time courses

We propose probabilistic timeboxes, which correspond to a specific class of Hidden Markov Models, that constitutes an established method in data mining. Since HMMs are a particular class of probabilistic graphical models we call our method Probabilistic Graphical Query Language. Its implementation was realized in the free software package pGQL. We evaluate its effectiveness in exploratory analysis on a yeast sporulation data set.We introduce a new approach to define dynamic, statistical queries on time course data. It supports an interactive exploration of reasonably large amounts of data and enables users without expert knowledge to specify fairly complex statistical models with ease. The expressivity of our approach is by its statistical nature greater and more robust with respect to amplitude and frequency fluctuation than the prior, deterministic timeboxes.The analysis of gene expression time courses e.g. from DNA microarrays is crucial in understanding dynamical biological processes such as cell cycle, cell development and cell response to external stimuli. Common data sets consist of 5-30 time points and hundreds or thousands of genes [1,2]. In the beginning investigators often explore their data by querying for certain qualitative and quantitative behaviors as an informative visual inspection of multivariate time points is indeed difficult. We define querying here as the evaluation of a set of conditions on time courses. The result of a query is a score for each time course that can be used to select a subset of time courses exposing behavior specified through the conditions. Among the characteristics of time courses is their variation in speed (cf. Figure 1d), i.e. delay of similar observations inducing uncertainty about exact time periods where measurements are expected to happen and phase shifts (c.f. Figure 1b). Generally, missing values, noise and outliers (cf. Figure 1c) can commonly be expected. In particular, gene expression time courses have only ver